What is the surface area of a rectangular pyramid with 10 mm, 8 mm, 12 mm, 15 mm
To find the surface area of a rectangular pyramid, we first need to calculate the area of the base and the area of the four triangular faces.
First, let's find the area of the base:
Area of base = length x width = 10 mm x 8 mm = 80 mm²
Next, let's find the area of the four triangular faces. To do this, we need to find the area of one of the triangular faces and then multiply it by 4 (since there are four triangular faces).
To find the area of one triangular face, we need to find the height of the pyramid. We can use the Pythagorean theorem to find the height:
h² = 12² + (1/2 x 10)²
h² = 144 + 25
h² = 169
h = 13 mm
Now, we can find the area of one triangular face:
Area of one triangular face = (1/2 x base x height) = (1/2 x 10 mm x 13 mm) = 65 mm²
Total surface area of the rectangular pyramid:
Surface area = area of base + area of four triangular faces
Surface area = 80 mm² + (4 x 65 mm²) = 80 mm² + 260 mm² = 340 mm²
Therefore, the surface area of the rectangular pyramid with dimensions 10 mm, 8 mm, 12 mm, and 15 mm is 340 mm².
That's wrong
I apologize for the error. Let's correct that.
The formula for the surface area of a rectangular pyramid is given by:
Surface area = base area + (1/2 x perimeter of base x slant height)
Given dimensions:
Length (l) = 10 mm
Width (w) = 8 mm
Height (h) = 12 mm
Slant height = 15 mm
First, let's calculate the area of the base:
Base area = l x w = 10 mm x 8 mm = 80 mm²
Next, calculate the perimeter of the base:
Perimeter of base = 2l + 2w = 2(10 mm) + 2(8 mm) = 20 mm + 16 mm = 36 mm
Now, calculate half the perimeter:
1/2 x perimeter of base = 1/2 x 36 mm = 18 mm
Now, use the formula for the surface area:
Surface area = base area + (1/2 x perimeter of base x slant height)
Surface area = 80 mm² + (1/2 x 36 mm x 15 mm)
Surface area = 80 mm² + 540 mm²
Surface area = 620 mm²
Therefore, the surface area of the rectangular pyramid with dimensions 10 mm, 8 mm, 12 mm, and 15 mm is 620 mm².